A196072 - OEIS

%I #8 May 08 2018 08:37:53

%S 0,1,2,0,6,2,8,12,10,32,26,58,82,104,204,238,424,606,870,1438,1952,

%T 3156,4602,6848,10634,15354,23794,35192,52844,80254,118744,180686,

%U 269382,405118,610576,911988,1377066,2061328,3099290,4659546,6984594,10512968

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,2,1,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 0's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 4's.

%C Column 2 of A196078.

%H R. H. Hardin, <a href="/A196072/b196072.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-2) +a(n-3) +2*a(n-5).

%F Empirical g.f.: x^2*(1 + 2*x - x^2 + 3*x^3) / (1 - x^2 - x^3 - 2*x^5). - _Colin Barker_, May 08 2018

%e All solutions for n=5:

%e ..2..2....2..2....1..0....1..0....0..1....0..1

%e ..2..2....2..2....3..1....3..1....1..3....1..3

%e ..0..1....1..0....1..1....1..0....0..1....1..1

%e ..1..3....3..1....1..3....2..2....2..2....3..1

%e ..0..1....1..0....0..1....2..2....2..2....1..0

%Y Cf. A196078.

%K nonn

%O 1,3

%A _R. H. Hardin_, Sep 27 2011